Probabilistic image processing based on the Q-Ising model by means of the mean-field method and loopy belief propagation

The framework is presented of Bayesian image restoration for multi-valued images by means of the Q-Ising model. Hyper parameters in the probabilistic model are determined so as to maximize the marginal likelihood. Practical algorithms are described based the conventional mean-field approximation and loopy belief propagation. We compare the results empirically with those provided by conventional filters and the new methods are found to be superior.